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will boiling water kill germs - GetMeFoodie

📅 April 30, 2026 👤 scraface

Apr 30, 2026

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📌 ثم $a + b = d(x + y) = 96$، لذا يجب أن يكون $d$ قاسمًا للعدد $96$.

📌 لتعظيم $d$، نختار أكبر قاسم للعدد $96$ بحيث يكون $x + y$ عددًا صحيحًا موجبًا، و$\gcd(x, y) = 1$.

📌 أكبر قاسم للعدد $96$ هو $48$، مع $x + y = 2$. الزوج $(x, y) = (1, 1)$ يحقق $\gcd(1,1)=1$.

📌 إذن، $a = 48 \cdot 1 = 48$، $b = 48 \cdot 1 = 48$، و$\gcd(a,b) = 48$.

📌 لذلك، أكبر قيمة ممكنة لـ $\gcd(a,b)$ هي $\boxed{48}$.

📌 السؤال: ما هو القاسم المشترك الأكبر للعددين $105$ و $165$؟

📌 الحل: نطبق خوارزمية إقليدس لإيجاد $\gcd(105, 165)$.

📌 = 1 \cdot 105 + 60

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